Page 290 - 1300 Math Formulas

CHAPTER 9. INTEGRAL CALCULUS

1130. iÉåÖíÜ=çÑ=~=`ìêîÉ=
β r β O  O O
∫



i = Çë = ∫ ê Ç ()Çíí = ∫  Çñ   +  Çó  +  Çò   ÇíI=
` α Çí α  Çí   Çí   Çí 
ïÜÉêÉ=`=á~=~=éáÉÅÉïáëÉ=ëãççíÜ=ÅìêîÉ=ÇÉëÅêáÄÉÇ=Äó=íÜÉ=éçëá-
r
íáçå=îÉÅíçê= () íê I= ≤α í ≤ β K=
=
fÑ=íÜÉ=ÅìêîÉ=`=áë=íïç-ÇáãÉåëáçå~äI=íÜÉå=
β r β  O  O
ê Ç
∫


i = Çë = ∫ ()Çíí = ∫  Çñ  +  Çó  ÇíK==
` α Çí α  Çí   Çí 
=
fÑ=íÜÉ=ÅìêîÉ=`=áë=íÜÉ=Öê~éÜ=çÑ=~=ÑìåÅíáçå= ó = Ñ ( ) ñ =áå=íÜÉ=ñó-
éä~åÉ=( ñ ≤ Ä I=íÜÉå==
)~ ≤
Ä  Çó  O
i = ∫ N +   Çñ K==
~  Çñ 
=
1131. iÉåÖíÜ=çÑ=~=`ìêîÉ=áå=mçä~ê=`ççêÇáå~íÉë=
β  O

i = ∫  Çê  + ê O Ç θI==
α  θÇ 
ïÜÉêÉ=íÜÉ=ÅìêîÉ=`=áë=ÖáîÉå=Äó=íÜÉ=Éèì~íáçå= = êê ( ) θ I=
α ≤ θ ≤ β =áå=éçä~ê=ÅççêÇáå~íÉëK===
=
1132. j~ëë=çÑ=~=táêÉ=
ã ∫ ( = ò I ó ) ρ I ñ Çë I==
`
ïÜÉêÉ= ( ρ ò I ) ó I ñ =áë=íÜÉ=ã~ëë=éÉê=ìåáí=äÉåÖíÜ=çÑ=íÜÉ=ïáêÉK=
=
fÑ=`=áë=~=ÅìêîÉ=é~ê~ãÉíêáòÉÇ=Äó=íÜÉ=îÉÅíçê=ÑìåÅíáçå
r
ê () í = ñ () ( ) ( ) íòIíóIí I==íÜÉå==íÜÉ==ã~ëë==Å~å==ÄÉ==ÅçãéìíÉÇ=Äó=
íÜÉ=Ñçêãìä~=

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